Let f be a function defined on the interval [a, b] with a > b. Assume that f ≥ 0 and that for each c > 0, the set x ∈ [a, b] | f(x) > c is finite. What can be concluded about the function f?
1) The function f is continuous on the interval [a, b].
2) The function f is differentiable on the interval [a, b].
3) The function f is bounded on the interval [a, b].
4) The function f is constant on the interval [a, b].